1. Field of the Invention
The present invention relates generally to wireless data systems, and in particular, to a method, apparatus, and article of manufacture for suppressing OFDM energy spectral density to minimize out-of-band emissions.
2. Description of the Related Art
Orthogonal Frequency Division Multiplexed (OFDM) signals are comprised of a set of subcarriers (also referred to as tones) which are constructed such that they are orthogonal to each other even though they overlap significantly in frequency. This is achieved as follows.
As far as the matched filter in the receiver is concerned (nuance here is that a cyclical prefix is added prior to transmission but removed prior to matched filter reception), each subcarrier, sk(t), during a symbol period, T, is a sinusoid of the form
            s      k        ⁡          (      t      )        =      {                                        sin            ⁡                          (                                                ω                  o                                ⁢                k                ⁢                                                                  ⁢                t                            )                                                            0            <            t            <            T                                                0                          otherwise                    It is easy to establish the orthogonality of such symbols by verifying
            ∫      0      T        ⁢                            s          i                ⁡                  (          t          )                    ⁢                        s          j                ⁡                  (          t          )                    ⁢                          ⁢              ⅆ        t              =      {                            C                                      i            =            j                                                0                                      i            ≠            j                              
In the time domain, the symbols are equal to a sinusoid times a rectangular time window of length T. Therefore in the frequency domain, the energy spectral density of each symbol is the convolution of a dirac delta function .(!.!o) with a Sinc( ) function, T Sinc(fT) (which has nulls at f=k=T 8k=0.1; 0.2; : : : ). If the subcarrier spacing fo is set at
      f    o    =                    ω        o                    2        ⁢                                  ⁢        π              =          1      /      T      then each subcarrier sits at the null of all other subcarriers. This is another way to recognize the orthogonality of the OFDM subcarriers. Thus, the baseband energy spectral density of the OFDM subcarrier sk(t) is given byS(f)=AikSinc(f−kfo)where Aik is the ith complex symbol which modulates the kth subcarrier during the ith symbol period. The composite OFDM energy spectral density of the ith symbol of all subcarriers is then just
      ∑    k    ⁢          ⁢            A              i        k              ⁢    Sin    ⁢                  ⁢          c      ⁡              (                  f          -                      k            ⁢                                                  ⁢                          f              o                                      )            
The relevance of this is that the Sinc function falls off very slowly with frequency. Since each of the subcarriers falls off slowly with frequency so does the aggregate OFDM signal as can been seen in FIG. 1A.
FIG. 1A shows a typical energy spectral density sample 100 from a 512 tone QPSK modulated OFDM signal. FIG. 1A shows the characteristic slow roll off. There are several methods employed to help mitigate this slow roll off. One of the primary techniques is to specify that a certain number, NGuard, of tones at the edge of the band are to be dedicated “guard” tones which are in fact not energized.
FIG. 1B depicts this technique as it is specified in the 802.16 specification. The 802.16 common air interface calls for a number of tones to be unused at the edges (and a “zeroed” DC tone as well). The exact number of tones specified to be “zeroed” is a function of the FFT order (i.e. the number of tones) and other system parameters.
FIG. 1B depicts graph 100 in comparison with graph 102, where graph 102 uses a typical 512 tone scenario where 40 left hand tones are un-energized and 39 right hand tones are un-energized (i.e., NGuard=79). Marked on FIGS. 1A and 1B are point 104 are tones 255 where the upper end of the OFDM spectrum stops if no guard tones are used and point 106, at tone 216, where the upper end of the OFDM spectrum stops if guard tones are used. FIG. 1B shows via graph 102 what happens to the energy spectral density of the upper band edge when the guard tones are deployed. In essence, the energy spectral density is decreased when the active cancellation of the present invention is used.
If an adjacent system would like to deploy close to this OFDM signal, the use of the guard tones drops the Out Of Band (OOB) emission by approximately 30 dB at band edge (i.e., at tone 256). It can also be seen from FIG. 1B that since the spectrum falls off rather slowly from the point 255 on, adding more guard tones would only provide modest further improvement. It is important to note the expense of these guard tones. The guard tones represent 79/512 of the spectrum or 15.4%. Thus, the use of guard tones represents 15.4% wasted bandwidth.
Perhaps one of the most typical approaches to controlling OOB roll off is to simply bandpass filter the composite OFDM signal. This is done in most systems which need more roll off than that which is provided by the utilization of guard tones. Bandpass filtering has two significant disadvantages beyond the mere fact that it adds hardware (HW) complexity. The first disadvantage occurs when significant edge of band roll off is required. First, note that the spectral occupancy of an OFDM tone is actually quite large (recall from Eq. (5) that significant tone energy extends over many tone intervals). Due to the large spectral extent, a brick wall filter will cut off a significant amount of the energy of the outer edge tones and thus directly reduce the Signal to Noise Ratio (SNR) of the output of the matched filter receiver for these tones. This then affects the Bit Error Rate (BER) performance of the outer tones. Furthermore, a brick wall filter may have significant differential group delay which will affect the orthogonality of the outer tones relative to the rest of the OFDM set. This can affect the (SNR) of the inner tones since the edge tones will contribute to their Inter-Carrier Interference (ICI). Thus the BER performance of the inner tones will suffer.
In the case of a large scale deployment, the use of bandpass filters has potentially an even greater cost. In a large scale deployment, the available spectrum can change slightly with time and with location due to regulatory changes or spectrum negotiations. HW bandpass filters can make it very expensive to adjust for changes in available spectrum. This lack of flexibility can have enormous financial impact. On the subscriber equipment side, the issue is somewhat less severe since these units tend not to be the main source of inter system interference (they transmit at lower power and have less line of sight because subscriber equipment is not tower mounted). Furthermore, subscriber equipment can be dynamically directed to not use frequencies near band edge. Finally, subscriber HW can be constructed based on a narrower tunable BW, unlike a base station which must transmit simultaneously over the entire available BW. The above discussion has bearing on the application of the new technique of the present invention. Employing the proposed technique only on the base stations (where it is most practical) may be sufficient. Finally, another technique which can be used to shape the OOB spectrum is to provide a temporal shaping of the guard time. In OFDM, the symbols are temporally extended through the use of a cyclical prefix. This prefix is used to help mitigate multipath effects and is removed by the receiver prior to matched filtering. The 802.11 specification recommends such shaping as a potential approach but does not insist upon its use if OOB spectral masks can be met without it. The 802.16 specification does not suggest cyclical prefix shaping. The cost of this technique is added HW/computational complexity.
Furthermore, some studies suggest that to get enough benefit from the guard time shaping the cyclical prefix would need to be extended beyond that which is required for multipath mitigation to allow for more gradual rise times. Such extension would directly impact system capacity since it reduces symbol rate without increasing SNR.
No mention of the contribution of spectral regrowth due to High Power Amplifier (HPA) nonlinearities herein. OFDM tends to have a relatively large Crest Factor (CF). This requires the power amplifiers used for OFDM applications to be operated with an Output Back Off (OBO) on the order of 10 dB. Note that guard tones will help contain spectral regrowth somewhat by narrowing the transmitted spectrum. In contrast, note that bandpass filtering generally must be done prior to the HPA. Therefore, bandpass filtering will not be very helpful if HPA induced spectral regrowth of the bandlimited signal produces unacceptable OBO. Guard time shaping will similarly not help if spectral regrowth dominates.
Spectral regrowth due to HPA nonlinearities must be primarily mitigated through some combination of sufficient output backoff and CF management through data and or guard tone manipulation. More exotically non-linear pre-distortion can be attempted.